A073804 Numbers k such that the number of divisors of k is greater than that of sigma(k).

4, 9, 16, 18, 25, 36, 48, 50, 64, 72, 80, 81, 100, 112, 144, 162, 180, 192, 196, 200, 208, 225, 240, 252, 256, 288, 289, 300, 320, 324, 336, 400, 432, 441, 448, 450, 468, 484, 512, 576, 578, 592, 624, 625, 648, 676, 700, 704, 720, 729, 768, 784, 800, 810, 832

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

Solutions to A000005(x) > A062068(x) = A000005(A000203(x)).

Example

k = 25: divisors(25) = {1,5,25}, 3 divisors; divisors(sigma(25)) = {1,31}, 2 divisors; 2 < 3, so 25 is a term.
k = 48: divisors(48) = {1,2,3,4,6,8,12,16,24,48}, 10 divisors; divisors(sigma(48)) = {1,2,4,31,62,124}, 6 divisors, 6 < 10 so 48 is a term.

Mathematica

Do[s=DivisorSigma[0, DivisorSigma[1, n]]; s0=DivisorSigma[0, n]; If[Greater[s0, s], Print[n]], {n, 1, 1000}]
Select[Range[900], DivisorSigma[0, #]>DivisorSigma[0, DivisorSigma[1, #]]&] (* Harvey P. Dale, Jan 18 2017 *)

Prog

(PARI) isok(k) = {my(f = factor(k)); numdiv(f) > numdiv(sigma(f)); } \\ Amiram Eldar, Mar 07 2025

Crossrefs

Cf. A000005, A000203, A062068, A073802, A073803, A037197.

Sequence in context: A235993 A102646 A104021 * A219364 A195212 A332443

Adjacent sequences: A073801 A073802 A073803 * A073805 A073806 A073807

Keyword

nonn,changed

Author

Labos Elemer, Aug 13 2002

Status

approved